Summation formulas for the function R1 [µ, δ, δ′; γ; ν, Ï„, z1, z2]
DOI:
https://doi.org/10.5269/bspm.64982Resumo
In this paper, we obtain finite and infinite summation formulas for Appell-type extension of $_pR_q(\nu,\tau;z)$ function, denoted as ${R_1}\left[ {\mu,\delta,\delta';\gamma;\nu ,\tau ,{z_1},{z_2}} \right]$ and confluent functions $R{\Phi _1}\left[ {\mu,\delta;\gamma;\nu ,\tau ,{z_1},{z_2}} \right], R{\Phi _2}\left[ {\delta,\delta';\gamma;\nu ,\tau ,{z_1},{z_2}} \right]$ and $R{\Phi _3}\left[ {\delta;\gamma;\nu ,\tau ,{z_1},{z_2}} \right].$
Referências
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6. Thakkar Y. M. and Shukla A. K., Some results involving the pRq(α, β; z) Function, J. Indian Math. Soc. 90(3-4), 329-342, 2023.
7. Thakkar Y. M. and Shukla A. K., Appell-Type Extension of The pRq(α, β; z) Function, Communicated for publication.
8. Thakkar Y. M. and Shukla A. K., Some Formulas For The Function R1 [µ, δ, δ′; γ; ν, Ï„, z1, z2], Communicated for publication.
9. Thakkar Y. M. and Shukla A. K., Some Formulas For The Function R3[µ, µâ€²Î´, δ′; γ; ν, Ï„, z1, z2], Advanced Studies: Euro-Tbilisi Mathematical Journal 16(3), 53–66, (2023).
10. Wang X., Infinite summatition formulas of double hypergeometric functions, Integral Transform Spec Funct., 27(5), 347-364 (2015).
2. Desai R. and Shukla A. K., Some results on function pRq(α, β; z), J. Math. Anal. Appl. 448, 187-197, (2017).
3. Desai R. and Shukla A. K., Note on the pRq(α, β; z) function, J. Indian Math. Soc. 88(3-4), 288-297, (2021).
4. Erdelyi A. and Bateman H., Higher Transcendental Functions vol. I, McGraw-Hill, New York, (1953).
5. Rainville E. D., Special Functions, The Macmillan Company, New York, (1960).
6. Thakkar Y. M. and Shukla A. K., Some results involving the pRq(α, β; z) Function, J. Indian Math. Soc. 90(3-4), 329-342, 2023.
7. Thakkar Y. M. and Shukla A. K., Appell-Type Extension of The pRq(α, β; z) Function, Communicated for publication.
8. Thakkar Y. M. and Shukla A. K., Some Formulas For The Function R1 [µ, δ, δ′; γ; ν, Ï„, z1, z2], Communicated for publication.
9. Thakkar Y. M. and Shukla A. K., Some Formulas For The Function R3[µ, µâ€²Î´, δ′; γ; ν, Ï„, z1, z2], Advanced Studies: Euro-Tbilisi Mathematical Journal 16(3), 53–66, (2023).
10. Wang X., Infinite summatition formulas of double hypergeometric functions, Integral Transform Spec Funct., 27(5), 347-364 (2015).
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2025-09-01
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Como Citar
Thakkar, Y. M., & SHUKLA, A. K. (2025). Summation formulas for the function R1 [µ, δ, δ′; γ; ν, Ï„, z1, z2]. Boletim Da Sociedade Paranaense De Matemática, 43, 1-9. https://doi.org/10.5269/bspm.64982
